Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
public class Funky  {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		List<Long> hash_Set = new ArrayList<Long>();
		Set<Long> hash_Set2 = new HashSet<Long>();
		long n = sc.nextLong();
		long res = 0;
		long dif = 0;
		
		boolean encontrado=false;
		
		for (long i = 1; i < 1000000000; i++) {
			res=calcular(i);
			hash_Set.add(res);
			
			if (res>=1000000000) {
				i=1000000000;
			}
		}
		
		hash_Set2.addAll(hash_Set);
		
		//System.out.println(hash_Set2);
		
		for (int i = 0; i < hash_Set.size(); i++) {
			dif = n - hash_Set.get(i);
			
			if (hash_Set2.contains(dif) ) {
				encontrado=true;
			}
		}
		
		
		if (encontrado) {
			System.out.println("YES");
		}else {
			System.out.println("NO");
		}
	}
	public static long calcular(long n) { 
		long res=0;
		res= (n*(n+1))/2;				
		return res; 
	}
}